TY - JOUR
T1 - Euler's constants for the Selberg and the Dedekind zeta functions
AU - Hashimoto, Yasufumi
AU - Iijima, Yasuyuki
AU - Kurokawa, Nobushige
AU - Wakayama, Masato
PY - 2004
Y1 - 2004
N2 - The purpose of this paper is to study an analogue of Euler's constant for the Selberg zeta functions of a compact Riemann surface and the Dedekind zeta function of an algebraic number field. Especially, we establish similar expressions of such Euler's constants as de la Vallée-Poussin obtained in 1896 for the Riemann zeta function. We also discuss, so to speak, higher Euler's constants and establish certain formulas concerning the power sums of essential zeroes of these zeta functions similar to Riemann's explicit formula.
AB - The purpose of this paper is to study an analogue of Euler's constant for the Selberg zeta functions of a compact Riemann surface and the Dedekind zeta function of an algebraic number field. Especially, we establish similar expressions of such Euler's constants as de la Vallée-Poussin obtained in 1896 for the Riemann zeta function. We also discuss, so to speak, higher Euler's constants and establish certain formulas concerning the power sums of essential zeroes of these zeta functions similar to Riemann's explicit formula.
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U2 - 10.36045/bbms/1102689119
DO - 10.36045/bbms/1102689119
M3 - Article
AN - SCOPUS:12944335053
SN - 1370-1444
VL - 11
SP - 493
EP - 516
JO - Bulletin of the Belgian Mathematical Society - Simon Stevin
JF - Bulletin of the Belgian Mathematical Society - Simon Stevin
IS - 4
ER -